scholarly journals Solvability for a New Class of Moore-Gibson-Thompson Equation with Viscoelastic Memory, Source Terms, and Integral Condition

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Salah Mahmoud Boulaaras ◽  
Abdelbaki Choucha ◽  
Djamel Ouchenane ◽  
Asma Alharbi ◽  
Mohamed Abdalla ◽  
...  
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Source Term ◽  
Mixed Boundary ◽  
Integral Condition ◽  
Mixed Boundary Value Problem ◽  
Uniqueness Of Solutions ◽  
Memory Kernel ◽  
New Class ◽  
Memory Source

This paper deals with the existence and uniqueness of solutions of a new class of Moore-Gibson-Thompson equation with respect to the nonlocal mixed boundary value problem, source term, and nonnegative memory kernel. Galerkin’s method was the main used tool for proving our result. This work is a generalization of recent homogenous work.

On a Dirichlet–Neumann–Third mixed boundary value problem for the Helmholtz equation

1983 ◽  
Vol 94 (3-4) ◽  
pp. 221-233 ◽  
Author(s):  
M. David
Keyword(s):  
Boundary Value Problem ◽  
Helmholtz Equation ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Uniqueness Theorems ◽  
Equivalent System ◽  
Mixed Boundary Value Problem ◽  
Existence And Uniqueness Theorems

SynopsisExistence and uniqueness theorems are proved for the solution of a Dirichlet-Neumann-Third mixed boundary value problem for the Helmholtz equation in ℝ3. The proofs make use of an equivalent system of two integral equations of the second kind.

scholarly journals Existence and uniqueness of solutions for a fractional boundary value problem on a graph

2014 ◽  
Vol 17 (2) ◽  
Author(s):  
John Graef ◽  
Lingju Kong ◽  
Min Wang
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mixed Boundary Conditions ◽  
Point Theory ◽  
Star Graph ◽  
Fractional Boundary Value Problem ◽  
Uniqueness Of Solutions

AbstractIn this paper, the authors consider a nonlinear fractional boundary value problem defined on a star graph. By using a transformation, an equivalent system of fractional boundary value problems with mixed boundary conditions is obtained. Then the existence and uniqueness of solutions are investigated by fixed point theory.

Integral Representations for the Solution of Dynamic Bending of a Plate with Displacement-Traction Boundary Data

2003 ◽  
Vol 10 (3) ◽  
pp. 467-480
Author(s):  
Igor Chudinovich ◽  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Boundary Data ◽  
Boundary Integral Equations ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Boundary Integral ◽  
Integral Representations ◽  
Transverse Shear Deformation ◽  
Uniqueness Of Solutions ◽  
Nonstationary Boundary

Abstract The existence of distributional solutions is investigated for the time-dependent bending of a plate with transverse shear deformation under mixed boundary conditions. The problem is then reduced to nonstationary boundary integral equations and the existence and uniqueness of solutions to the latter are studied in appropriate Sobolev spaces.

scholarly journals Existence and uniqueness of positive solutions for nonlinear fractional mixed problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alberto Cabada ◽  
Om Kalthoum Wanassi
Keyword(s):  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Mixed Boundary ◽  
Point Theory ◽  
Uniqueness Of Solutions ◽  
Nonlinear Part ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Exhaustive Study ◽  
The Banach Contraction Principle

Abstract This paper is devoted to study the existence and uniqueness of solutions of a one parameter family of nonlinear Riemann–Liouville fractional differential equations with mixed boundary value conditions. An exhaustive study of the sign of the related Green’s function is carried out. Under suitable assumptions on the asymptotic behavior of the nonlinear part of the equation at zero and at infinity, and by application of the fixed point theory of compact operators defined in suitable cones, it is proved that there exists at least one solution of the considered problem. Moreover, the method of lower and upper solutions is developed and the existence of solutions is deduced by a combination of both techniques. In particular cases, the Banach contraction principle is used to ensure the uniqueness of solutions.

scholarly journals Existence and uniqueness of solutions for a mixed p-Laplace boundary value problem involving fractional derivatives

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuqi Wang ◽  
Zhanbing Bai
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Novel Approach ◽  
Banach Contraction ◽  
Left And Right ◽  
Banach Contraction Mapping Principle

AbstractIn this article, the existence and uniqueness of solutions for a multi-point fractional boundary value problem involving two different left and right fractional derivatives with p-Laplace operator is studied. A novel approach is used to acquire the desired results, and the core of the method is Banach contraction mapping principle. Finally, an example is given to verify the results.

Sign in / Sign up

Export Citation Format

Share Document